On a Z-Transformation Approach to a Continuous-Time Markov Process with Nonfixed Transition Rates

The paper presents z-transform as a method of functional transformation with
respect to its theory and properties in dealing with discrete systems. We therefore
obtain the absolute state probabilities as a solution of a differential equation
corresponding to a given Birth-and–Death process via the z-transform, and
deduce the equivalent stationary state probabilities of the system.